# Memorization and Malign Generalization in Conditional Diffusion Models with Random Features

arXiv: https://arxiv.org/abs/2610.11288 · HTML: https://mlsanity.com/paper/2610.11288/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 14 of its 66 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 14 of 14)

- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [A Survey on Audio Diffusion Models: Text To Speech Synthesis and Enhancement in Generative AI](https://mlsanity.com/paper/2303.13336/) (2023)
- [Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions](https://mlsanity.com/paper/2409.18804/) (2024)
- [Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory](https://mlsanity.com/paper/2403.11968/) (2024)
- [A Reproducible Extraction of Training Images from Diffusion Models](https://mlsanity.com/paper/2305.08694/) (2023)
- [ELF: Embedded Language Flows](https://mlsanity.com/paper/2605.10938/) (2026)
- [The Emergence of Reproducibility and Generalizability in Diffusion Models](https://mlsanity.com/paper/2310.05264/) (2023)
- [Taking a Big Step: Large Learning Rates in Denoising Score Matching Prevent Memorization](https://mlsanity.com/paper/2502.03435/) (2025)
- [Generalization Dynamics of Linear Diffusion Models](https://mlsanity.com/paper/2505.24769/) (2025)
- [Asymptotic Learning Curves for Diffusion Models with Random Features Score and Manifold Data](https://mlsanity.com/paper/2603.22962/) (2026)
- [Benign Overfitting Does Not Occur in Diffusion Models](https://mlsanity.com/paper/2607.02671/) (2026)
- [Generalization, memorization, and overfitting for diffusion models trained in the lazy high-dimensional regime](https://mlsanity.com/paper/2608.23938/) (2026)
- [Double Descent and Malign Overfitting in Diffusion Models](https://mlsanity.com/paper/2609.26392/) (2026)

## Abstract (arXiv)

Conditional diffusion models generate diverse, novel, and high-quality samples under prescribed conditions. However, theoretical understanding of their memorization and generalization remains limited, while recent works have characterized these behaviors primarily in unconditional settings. In this work, we analyze a random-feature conditional score model in the high-dimensional proportional limit, deriving asymptotic expressions for training and test losses. By decomposing the test loss, we show that in the overparameterized regime, increasing model width improves prediction of the condition-dependent mean while reducing within-condition prediction variance, a phenomenon we term "malign generalization." Furthermore, analyzing the training loss reveals that more informative conditions lead to memorization of training samples at smaller widths. These theoretical findings are supported by experiments with U-Net architectures on realistic data.